We derive the gravitational constant from the Bootstrap framework. Gravity emerges from the −1/12 = −1/D(D+1) turning force — the attractive bias inherited from the first +1 of Grandi's series. The gravitational hierarchy follows: ln(m_P/m_e) = (e⁵+2π)/3 − 1/27, achieving 99.999% agreement with measurement. The formula parallels the fine structure constant derivation, with e⁵ as the leading term in both. The correction term 1/27 = 1/D³ connects to the lattice response factor 3√3 = √27, which appears in dark matter phenomenology. The number 27 = D³ = (3√3)² thus bridges Planck-scale gravity to galactic dynamics through identical D = 3 geometry. G is derived to four significant figures with zero free parameters.